A standardized test is given to a sixth grade class. Historically, the test scores have had a standard deviation of 25 . The superintendent believes that the standard deviation of performance may have recently changed. She randomly sampled 29 students and found a mean of 155 with a standard deviation of 38.5111. Is there evidence that the standard deviation of test scores has decreased at the =0.005 level? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision

Step 5 of 5: What is the conclusion?